Two diamonds begin a free fall from rest from the same height, 1.0 s apart. How long after the

step 1 Okay, so we've got two diamonds falling, one second after the other. How long will it take for t

Two diamonds begin a free fall from rest from the same...

Key Concepts

Free Fall

Free fall refers to the motion of an object solely under the influence of gravity. In such cases, the only acceleration that acts on the object is the gravitational acceleration, which is constant and directed downwards. This concept is essential for analyzing the motion of any object in a gravitational field without the interference of other forces.

Kinematic Equations

Kinematic equations describe the motion of objects experiencing constant acceleration, such as during free fall. These equations relate displacement, initial velocity, acceleration, and time, allowing one to compute any missing variable when the others are known. They are fundamental in solving problems in mechanics involving uniformly accelerated motion.

Relative Motion

Relative motion involves analyzing the movement of one object with respect to another. In problems where two objects are moving, often starting at different times, calculating the relative distance between them requires considering the difference in their individual displacements over time. This approach is crucial when determining when the separation between the objects reaches a specified value.

Quadratic Equations

The process of solving for time in kinematics leading to a specified condition often results in a quadratic equation. Quadratic equations must be analyzed for their physical relevance, and the appropriate solution is chosen based on the context of the motion. The ability to set up and solve these equations is a key mathematical tool in resolving problems involving free fall and other uniformly accelerated motions.

Transcript

00:01 Okay, so we've got two diamonds falling, one second after the other.

00:06 How long will it take for the two diamonds to be 10 meters apart? well, for the first diamond, y is going to equal y initial, which i'll call zero, plus v initial t, which is also zero, plus one -half a t squared.

00:35 Now, for the other diamond, y equals one -half -a, t -minus -1 squared.

00:46 But we want 10 to be, oops, y2 minus y -1.

01:01 One -half -a, t -minus 1 squared.

01:09 No, no, no, it would be, no, yeah, that, kind of makes sense, except it's going to be, yeah, that's right, that's right.

01:28 A is g, a is g, okay, and then minus one -half g t squared.

01:36 Okay, so we can factor out the one -half in the g, multiply by two over g on both sides, and that's going to give me 20 over -year.

01:50 G equals t minus one squared minus t squared um using the foil method for for the t minus one squared gives me t squared minus two t plus one and then we still have the minus t squared which cancels out so 20 g is negative 2 t plus 1 okay um 20 over g minus 1 is going to equal negative 2 t negative to t so t is going to be 20 20 over g minus 1 over negative 2.

03:11 So g equals 9 .81, 20 over g minus 1 over negative 2.

03:29 That gives me 0 .52 seconds, and i'm trying to look for significant digits.

03:41 T equals, i actually got negative, 0 .52 seconds.

03:49 So now i want to look back and figure out why i got negative.

03:54 I was debating this at the beginning.

03:59 Y2, which is the one that's going to be afterwards, minus y1, which is the one that's drawn first, well, that should be negative 10.

04:12 So, and then i wrote in y2 minus y1.

04:16 So this should have been negative.

04:19 This should have been negative.

04:21 Okay...